# Properties

 Label 722.2.c.c.653.1 Level $722$ Weight $2$ Character 722.653 Analytic conductor $5.765$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(429,722)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("722.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$722 = 2 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 722.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$5.76519902594$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 38) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 653.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 722.653 Dual form 722.2.c.c.429.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} -6.00000 q^{11} -1.00000 q^{12} +(2.50000 - 4.33013i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} -2.00000 q^{18} +(-0.500000 - 0.866025i) q^{21} +(3.00000 + 5.19615i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} -5.00000 q^{26} +5.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(4.50000 - 7.79423i) q^{29} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(-1.50000 + 2.59808i) q^{34} +(1.00000 + 1.73205i) q^{36} -2.00000 q^{37} +5.00000 q^{39} +(-0.500000 + 0.866025i) q^{42} +(-4.00000 - 6.92820i) q^{43} +(3.00000 - 5.19615i) q^{44} +3.00000 q^{46} +(0.500000 - 0.866025i) q^{48} -6.00000 q^{49} -5.00000 q^{50} +(1.50000 - 2.59808i) q^{51} +(2.50000 + 4.33013i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(-2.50000 - 4.33013i) q^{54} -1.00000 q^{56} -9.00000 q^{58} +(4.50000 + 7.79423i) q^{59} +(5.00000 - 8.66025i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(2.50000 - 4.33013i) q^{67} +3.00000 q^{68} -3.00000 q^{69} +(-3.00000 - 5.19615i) q^{71} +(1.00000 - 1.73205i) q^{72} +(3.50000 + 6.06218i) q^{73} +(1.00000 + 1.73205i) q^{74} +5.00000 q^{75} +6.00000 q^{77} +(-2.50000 - 4.33013i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -6.00000 q^{83} +1.00000 q^{84} +(-4.00000 + 6.92820i) q^{86} +9.00000 q^{87} -6.00000 q^{88} +(-6.00000 + 10.3923i) q^{89} +(-2.50000 + 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} +(2.00000 + 3.46410i) q^{93} -1.00000 q^{96} +(-5.00000 - 8.66025i) q^{97} +(3.00000 + 5.19615i) q^{98} +(-6.00000 + 10.3923i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} + q^{3} - q^{4} + q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10})$$ 2 * q - q^2 + q^3 - q^4 + q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 $$2 q - q^{2} + q^{3} - q^{4} + q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 12 q^{11} - 2 q^{12} + 5 q^{13} + q^{14} - q^{16} - 3 q^{17} - 4 q^{18} - q^{21} + 6 q^{22} - 3 q^{23} + q^{24} + 5 q^{25} - 10 q^{26} + 10 q^{27} + q^{28} + 9 q^{29} + 8 q^{31} - q^{32} - 6 q^{33} - 3 q^{34} + 2 q^{36} - 4 q^{37} + 10 q^{39} - q^{42} - 8 q^{43} + 6 q^{44} + 6 q^{46} + q^{48} - 12 q^{49} - 10 q^{50} + 3 q^{51} + 5 q^{52} - 3 q^{53} - 5 q^{54} - 2 q^{56} - 18 q^{58} + 9 q^{59} + 10 q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} - 6 q^{66} + 5 q^{67} + 6 q^{68} - 6 q^{69} - 6 q^{71} + 2 q^{72} + 7 q^{73} + 2 q^{74} + 10 q^{75} + 12 q^{77} - 5 q^{78} - 10 q^{79} - q^{81} - 12 q^{83} + 2 q^{84} - 8 q^{86} + 18 q^{87} - 12 q^{88} - 12 q^{89} - 5 q^{91} - 3 q^{92} + 4 q^{93} - 2 q^{96} - 10 q^{97} + 6 q^{98} - 12 q^{99}+O(q^{100})$$ 2 * q - q^2 + q^3 - q^4 + q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 12 * q^11 - 2 * q^12 + 5 * q^13 + q^14 - q^16 - 3 * q^17 - 4 * q^18 - q^21 + 6 * q^22 - 3 * q^23 + q^24 + 5 * q^25 - 10 * q^26 + 10 * q^27 + q^28 + 9 * q^29 + 8 * q^31 - q^32 - 6 * q^33 - 3 * q^34 + 2 * q^36 - 4 * q^37 + 10 * q^39 - q^42 - 8 * q^43 + 6 * q^44 + 6 * q^46 + q^48 - 12 * q^49 - 10 * q^50 + 3 * q^51 + 5 * q^52 - 3 * q^53 - 5 * q^54 - 2 * q^56 - 18 * q^58 + 9 * q^59 + 10 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 - 6 * q^66 + 5 * q^67 + 6 * q^68 - 6 * q^69 - 6 * q^71 + 2 * q^72 + 7 * q^73 + 2 * q^74 + 10 * q^75 + 12 * q^77 - 5 * q^78 - 10 * q^79 - q^81 - 12 * q^83 + 2 * q^84 - 8 * q^86 + 18 * q^87 - 12 * q^88 - 12 * q^89 - 5 * q^91 - 3 * q^92 + 4 * q^93 - 2 * q^96 - 10 * q^97 + 6 * q^98 - 12 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$$.

 $$n$$ $$363$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i $$-0.0734519\pi$$
−0.684819 + 0.728714i $$0.740119\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$6$$ 0.500000 0.866025i 0.204124 0.353553i
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 1.73205i 0.333333 0.577350i
$$10$$ 0 0
$$11$$ −6.00000 −1.80907 −0.904534 0.426401i $$-0.859781\pi$$
−0.904534 + 0.426401i $$0.859781\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 2.50000 4.33013i 0.693375 1.20096i −0.277350 0.960769i $$-0.589456\pi$$
0.970725 0.240192i $$-0.0772105\pi$$
$$14$$ 0.500000 + 0.866025i 0.133631 + 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i $$-0.285189\pi$$
−0.988583 + 0.150675i $$0.951855\pi$$
$$18$$ −2.00000 −0.471405
$$19$$ 0 0
$$20$$ 0 0
$$21$$ −0.500000 0.866025i −0.109109 0.188982i
$$22$$ 3.00000 + 5.19615i 0.639602 + 1.10782i
$$23$$ −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i $$-0.934591\pi$$
0.666190 + 0.745782i $$0.267924\pi$$
$$24$$ 0.500000 + 0.866025i 0.102062 + 0.176777i
$$25$$ 2.50000 4.33013i 0.500000 0.866025i
$$26$$ −5.00000 −0.980581
$$27$$ 5.00000 0.962250
$$28$$ 0.500000 0.866025i 0.0944911 0.163663i
$$29$$ 4.50000 7.79423i 0.835629 1.44735i −0.0578882 0.998323i $$-0.518437\pi$$
0.893517 0.449029i $$-0.148230\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ −3.00000 5.19615i −0.522233 0.904534i
$$34$$ −1.50000 + 2.59808i −0.257248 + 0.445566i
$$35$$ 0 0
$$36$$ 1.00000 + 1.73205i 0.166667 + 0.288675i
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 0 0
$$39$$ 5.00000 0.800641
$$40$$ 0 0
$$41$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$42$$ −0.500000 + 0.866025i −0.0771517 + 0.133631i
$$43$$ −4.00000 6.92820i −0.609994 1.05654i −0.991241 0.132068i $$-0.957838\pi$$
0.381246 0.924473i $$-0.375495\pi$$
$$44$$ 3.00000 5.19615i 0.452267 0.783349i
$$45$$ 0 0
$$46$$ 3.00000 0.442326
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 0.500000 0.866025i 0.0721688 0.125000i
$$49$$ −6.00000 −0.857143
$$50$$ −5.00000 −0.707107
$$51$$ 1.50000 2.59808i 0.210042 0.363803i
$$52$$ 2.50000 + 4.33013i 0.346688 + 0.600481i
$$53$$ −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i $$-0.899391\pi$$
0.744423 + 0.667708i $$0.232725\pi$$
$$54$$ −2.50000 4.33013i −0.340207 0.589256i
$$55$$ 0 0
$$56$$ −1.00000 −0.133631
$$57$$ 0 0
$$58$$ −9.00000 −1.18176
$$59$$ 4.50000 + 7.79423i 0.585850 + 1.01472i 0.994769 + 0.102151i $$0.0325726\pi$$
−0.408919 + 0.912571i $$0.634094\pi$$
$$60$$ 0 0
$$61$$ 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i $$-0.612191\pi$$
0.985391 0.170305i $$-0.0544754\pi$$
$$62$$ −2.00000 3.46410i −0.254000 0.439941i
$$63$$ −1.00000 + 1.73205i −0.125988 + 0.218218i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −3.00000 + 5.19615i −0.369274 + 0.639602i
$$67$$ 2.50000 4.33013i 0.305424 0.529009i −0.671932 0.740613i $$-0.734535\pi$$
0.977356 + 0.211604i $$0.0678686\pi$$
$$68$$ 3.00000 0.363803
$$69$$ −3.00000 −0.361158
$$70$$ 0 0
$$71$$ −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i $$-0.282538\pi$$
−0.987294 + 0.158901i $$0.949205\pi$$
$$72$$ 1.00000 1.73205i 0.117851 0.204124i
$$73$$ 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i $$-0.0323196\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 1.00000 + 1.73205i 0.116248 + 0.201347i
$$75$$ 5.00000 0.577350
$$76$$ 0 0
$$77$$ 6.00000 0.683763
$$78$$ −2.50000 4.33013i −0.283069 0.490290i
$$79$$ −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i $$-0.976489\pi$$
0.434730 0.900561i $$-0.356844\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ 1.00000 0.109109
$$85$$ 0 0
$$86$$ −4.00000 + 6.92820i −0.431331 + 0.747087i
$$87$$ 9.00000 0.964901
$$88$$ −6.00000 −0.639602
$$89$$ −6.00000 + 10.3923i −0.635999 + 1.10158i 0.350304 + 0.936636i $$0.386078\pi$$
−0.986303 + 0.164946i $$0.947255\pi$$
$$90$$ 0 0
$$91$$ −2.50000 + 4.33013i −0.262071 + 0.453921i
$$92$$ −1.50000 2.59808i −0.156386 0.270868i
$$93$$ 2.00000 + 3.46410i 0.207390 + 0.359211i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ −5.00000 8.66025i −0.507673 0.879316i −0.999961 0.00888289i $$-0.997172\pi$$
0.492287 0.870433i $$-0.336161\pi$$
$$98$$ 3.00000 + 5.19615i 0.303046 + 0.524891i
$$99$$ −6.00000 + 10.3923i −0.603023 + 1.04447i
$$100$$ 2.50000 + 4.33013i 0.250000 + 0.433013i
$$101$$ −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i $$0.519872\pi$$
−0.833143 + 0.553058i $$0.813461\pi$$
$$102$$ −3.00000 −0.297044
$$103$$ −14.0000 −1.37946 −0.689730 0.724066i $$-0.742271\pi$$
−0.689730 + 0.724066i $$0.742271\pi$$
$$104$$ 2.50000 4.33013i 0.245145 0.424604i
$$105$$ 0 0
$$106$$ 3.00000 0.291386
$$107$$ 9.00000 0.870063 0.435031 0.900415i $$-0.356737\pi$$
0.435031 + 0.900415i $$0.356737\pi$$
$$108$$ −2.50000 + 4.33013i −0.240563 + 0.416667i
$$109$$ 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i $$0.00994332\pi$$
−0.472708 + 0.881219i $$0.656723\pi$$
$$110$$ 0 0
$$111$$ −1.00000 1.73205i −0.0949158 0.164399i
$$112$$ 0.500000 + 0.866025i 0.0472456 + 0.0818317i
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 4.50000 + 7.79423i 0.417815 + 0.723676i
$$117$$ −5.00000 8.66025i −0.462250 0.800641i
$$118$$ 4.50000 7.79423i 0.414259 0.717517i
$$119$$ 1.50000 + 2.59808i 0.137505 + 0.238165i
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ −10.0000 −0.905357
$$123$$ 0 0
$$124$$ −2.00000 + 3.46410i −0.179605 + 0.311086i
$$125$$ 0 0
$$126$$ 2.00000 0.178174
$$127$$ 1.00000 1.73205i 0.0887357 0.153695i −0.818241 0.574875i $$-0.805051\pi$$
0.906977 + 0.421180i $$0.138384\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 4.00000 6.92820i 0.352180 0.609994i
$$130$$ 0 0
$$131$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$132$$ 6.00000 0.522233
$$133$$ 0 0
$$134$$ −5.00000 −0.431934
$$135$$ 0 0
$$136$$ −1.50000 2.59808i −0.128624 0.222783i
$$137$$ 4.50000 7.79423i 0.384461 0.665906i −0.607233 0.794524i $$-0.707721\pi$$
0.991694 + 0.128618i $$0.0410540\pi$$
$$138$$ 1.50000 + 2.59808i 0.127688 + 0.221163i
$$139$$ 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i $$-0.779074\pi$$
0.938293 + 0.345843i $$0.112407\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −3.00000 + 5.19615i −0.251754 + 0.436051i
$$143$$ −15.0000 + 25.9808i −1.25436 + 2.17262i
$$144$$ −2.00000 −0.166667
$$145$$ 0 0
$$146$$ 3.50000 6.06218i 0.289662 0.501709i
$$147$$ −3.00000 5.19615i −0.247436 0.428571i
$$148$$ 1.00000 1.73205i 0.0821995 0.142374i
$$149$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$150$$ −2.50000 4.33013i −0.204124 0.353553i
$$151$$ 10.0000 0.813788 0.406894 0.913475i $$-0.366612\pi$$
0.406894 + 0.913475i $$0.366612\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ −3.00000 5.19615i −0.241747 0.418718i
$$155$$ 0 0
$$156$$ −2.50000 + 4.33013i −0.200160 + 0.346688i
$$157$$ 11.0000 + 19.0526i 0.877896 + 1.52056i 0.853646 + 0.520854i $$0.174386\pi$$
0.0242497 + 0.999706i $$0.492280\pi$$
$$158$$ −5.00000 + 8.66025i −0.397779 + 0.688973i
$$159$$ −3.00000 −0.237915
$$160$$ 0 0
$$161$$ 1.50000 2.59808i 0.118217 0.204757i
$$162$$ −0.500000 + 0.866025i −0.0392837 + 0.0680414i
$$163$$ 20.0000 1.56652 0.783260 0.621694i $$-0.213555\pi$$
0.783260 + 0.621694i $$0.213555\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 3.00000 + 5.19615i 0.232845 + 0.403300i
$$167$$ 6.00000 10.3923i 0.464294 0.804181i −0.534875 0.844931i $$-0.679641\pi$$
0.999169 + 0.0407502i $$0.0129748\pi$$
$$168$$ −0.500000 0.866025i −0.0385758 0.0668153i
$$169$$ −6.00000 10.3923i −0.461538 0.799408i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 8.00000 0.609994
$$173$$ 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i $$-0.0934200\pi$$
−0.729155 + 0.684349i $$0.760087\pi$$
$$174$$ −4.50000 7.79423i −0.341144 0.590879i
$$175$$ −2.50000 + 4.33013i −0.188982 + 0.327327i
$$176$$ 3.00000 + 5.19615i 0.226134 + 0.391675i
$$177$$ −4.50000 + 7.79423i −0.338241 + 0.585850i
$$178$$ 12.0000 0.899438
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 1.00000 1.73205i 0.0743294 0.128742i −0.826465 0.562988i $$-0.809652\pi$$
0.900794 + 0.434246i $$0.142985\pi$$
$$182$$ 5.00000 0.370625
$$183$$ 10.0000 0.739221
$$184$$ −1.50000 + 2.59808i −0.110581 + 0.191533i
$$185$$ 0 0
$$186$$ 2.00000 3.46410i 0.146647 0.254000i
$$187$$ 9.00000 + 15.5885i 0.658145 + 1.13994i
$$188$$ 0 0
$$189$$ −5.00000 −0.363696
$$190$$ 0 0
$$191$$ 3.00000 0.217072 0.108536 0.994092i $$-0.465384\pi$$
0.108536 + 0.994092i $$0.465384\pi$$
$$192$$ 0.500000 + 0.866025i 0.0360844 + 0.0625000i
$$193$$ 7.00000 + 12.1244i 0.503871 + 0.872730i 0.999990 + 0.00447566i $$0.00142465\pi$$
−0.496119 + 0.868255i $$0.665242\pi$$
$$194$$ −5.00000 + 8.66025i −0.358979 + 0.621770i
$$195$$ 0 0
$$196$$ 3.00000 5.19615i 0.214286 0.371154i
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 12.0000 0.852803
$$199$$ −5.50000 + 9.52628i −0.389885 + 0.675300i −0.992434 0.122782i $$-0.960818\pi$$
0.602549 + 0.798082i $$0.294152\pi$$
$$200$$ 2.50000 4.33013i 0.176777 0.306186i
$$201$$ 5.00000 0.352673
$$202$$ 18.0000 1.26648
$$203$$ −4.50000 + 7.79423i −0.315838 + 0.547048i
$$204$$ 1.50000 + 2.59808i 0.105021 + 0.181902i
$$205$$ 0 0
$$206$$ 7.00000 + 12.1244i 0.487713 + 0.844744i
$$207$$ 3.00000 + 5.19615i 0.208514 + 0.361158i
$$208$$ −5.00000 −0.346688
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i $$-0.111609\pi$$
−0.767049 + 0.641588i $$0.778276\pi$$
$$212$$ −1.50000 2.59808i −0.103020 0.178437i
$$213$$ 3.00000 5.19615i 0.205557 0.356034i
$$214$$ −4.50000 7.79423i −0.307614 0.532803i
$$215$$ 0 0
$$216$$ 5.00000 0.340207
$$217$$ −4.00000 −0.271538
$$218$$ 5.50000 9.52628i 0.372507 0.645201i
$$219$$ −3.50000 + 6.06218i −0.236508 + 0.409644i
$$220$$ 0 0
$$221$$ −15.0000 −1.00901
$$222$$ −1.00000 + 1.73205i −0.0671156 + 0.116248i
$$223$$ 13.0000 + 22.5167i 0.870544 + 1.50783i 0.861435 + 0.507869i $$0.169566\pi$$
0.00910984 + 0.999959i $$0.497100\pi$$
$$224$$ 0.500000 0.866025i 0.0334077 0.0578638i
$$225$$ −5.00000 8.66025i −0.333333 0.577350i
$$226$$ 3.00000 + 5.19615i 0.199557 + 0.345643i
$$227$$ 15.0000 0.995585 0.497792 0.867296i $$-0.334144\pi$$
0.497792 + 0.867296i $$0.334144\pi$$
$$228$$ 0 0
$$229$$ −22.0000 −1.45380 −0.726900 0.686743i $$-0.759040\pi$$
−0.726900 + 0.686743i $$0.759040\pi$$
$$230$$ 0 0
$$231$$ 3.00000 + 5.19615i 0.197386 + 0.341882i
$$232$$ 4.50000 7.79423i 0.295439 0.511716i
$$233$$ 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i $$-0.103697\pi$$
−0.750867 + 0.660454i $$0.770364\pi$$
$$234$$ −5.00000 + 8.66025i −0.326860 + 0.566139i
$$235$$ 0 0
$$236$$ −9.00000 −0.585850
$$237$$ 5.00000 8.66025i 0.324785 0.562544i
$$238$$ 1.50000 2.59808i 0.0972306 0.168408i
$$239$$ −21.0000 −1.35838 −0.679189 0.733964i $$-0.737668\pi$$
−0.679189 + 0.733964i $$0.737668\pi$$
$$240$$ 0 0
$$241$$ 4.00000 6.92820i 0.257663 0.446285i −0.707953 0.706260i $$-0.750381\pi$$
0.965615 + 0.259975i $$0.0837143\pi$$
$$242$$ −12.5000 21.6506i −0.803530 1.39176i
$$243$$ 8.00000 13.8564i 0.513200 0.888889i
$$244$$ 5.00000 + 8.66025i 0.320092 + 0.554416i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 4.00000 0.254000
$$249$$ −3.00000 5.19615i −0.190117 0.329293i
$$250$$ 0 0
$$251$$ −3.00000 + 5.19615i −0.189358 + 0.327978i −0.945036 0.326965i $$-0.893974\pi$$
0.755678 + 0.654943i $$0.227307\pi$$
$$252$$ −1.00000 1.73205i −0.0629941 0.109109i
$$253$$ 9.00000 15.5885i 0.565825 0.980038i
$$254$$ −2.00000 −0.125491
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 6.00000 10.3923i 0.374270 0.648254i −0.615948 0.787787i $$-0.711227\pi$$
0.990217 + 0.139533i $$0.0445601\pi$$
$$258$$ −8.00000 −0.498058
$$259$$ 2.00000 0.124274
$$260$$ 0 0
$$261$$ −9.00000 15.5885i −0.557086 0.964901i
$$262$$ 0 0
$$263$$ −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i $$-0.901515\pi$$
0.212565 0.977147i $$-0.431818\pi$$
$$264$$ −3.00000 5.19615i −0.184637 0.319801i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −12.0000 −0.734388
$$268$$ 2.50000 + 4.33013i 0.152712 + 0.264505i
$$269$$ −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i $$-0.225219\pi$$
−0.942871 + 0.333157i $$0.891886\pi$$
$$270$$ 0 0
$$271$$ −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i $$-0.275099\pi$$
−0.983312 + 0.181928i $$0.941766\pi$$
$$272$$ −1.50000 + 2.59808i −0.0909509 + 0.157532i
$$273$$ −5.00000 −0.302614
$$274$$ −9.00000 −0.543710
$$275$$ −15.0000 + 25.9808i −0.904534 + 1.56670i
$$276$$ 1.50000 2.59808i 0.0902894 0.156386i
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ −4.00000 −0.239904
$$279$$ 4.00000 6.92820i 0.239474 0.414781i
$$280$$ 0 0
$$281$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$282$$ 0 0
$$283$$ 11.0000 + 19.0526i 0.653882 + 1.13256i 0.982173 + 0.187980i $$0.0601941\pi$$
−0.328291 + 0.944577i $$0.606473\pi$$
$$284$$ 6.00000 0.356034
$$285$$ 0 0
$$286$$ 30.0000 1.77394
$$287$$ 0 0
$$288$$ 1.00000 + 1.73205i 0.0589256 + 0.102062i
$$289$$ 4.00000 6.92820i 0.235294 0.407541i
$$290$$ 0 0
$$291$$ 5.00000 8.66025i 0.293105 0.507673i
$$292$$ −7.00000 −0.409644
$$293$$ 21.0000 1.22683 0.613417 0.789760i $$-0.289795\pi$$
0.613417 + 0.789760i $$0.289795\pi$$
$$294$$ −3.00000 + 5.19615i −0.174964 + 0.303046i
$$295$$ 0 0
$$296$$ −2.00000 −0.116248
$$297$$ −30.0000 −1.74078
$$298$$ 0 0
$$299$$ 7.50000 + 12.9904i 0.433736 + 0.751253i
$$300$$ −2.50000 + 4.33013i −0.144338 + 0.250000i
$$301$$ 4.00000 + 6.92820i 0.230556 + 0.399335i
$$302$$ −5.00000 8.66025i −0.287718 0.498342i
$$303$$ −18.0000 −1.03407
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 3.00000 + 5.19615i 0.171499 + 0.297044i
$$307$$ 10.0000 + 17.3205i 0.570730 + 0.988534i 0.996491 + 0.0836980i $$0.0266731\pi$$
−0.425761 + 0.904836i $$0.639994\pi$$
$$308$$ −3.00000 + 5.19615i −0.170941 + 0.296078i
$$309$$ −7.00000 12.1244i −0.398216 0.689730i
$$310$$ 0 0
$$311$$ −21.0000 −1.19080 −0.595400 0.803429i $$-0.703007\pi$$
−0.595400 + 0.803429i $$0.703007\pi$$
$$312$$ 5.00000 0.283069
$$313$$ 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i $$-0.652902\pi$$
0.999065 0.0432311i $$-0.0137652\pi$$
$$314$$ 11.0000 19.0526i 0.620766 1.07520i
$$315$$ 0 0
$$316$$ 10.0000 0.562544
$$317$$ −4.50000 + 7.79423i −0.252745 + 0.437767i −0.964281 0.264883i $$-0.914667\pi$$
0.711535 + 0.702650i $$0.248000\pi$$
$$318$$ 1.50000 + 2.59808i 0.0841158 + 0.145693i
$$319$$ −27.0000 + 46.7654i −1.51171 + 2.61836i
$$320$$ 0 0
$$321$$ 4.50000 + 7.79423i 0.251166 + 0.435031i
$$322$$ −3.00000 −0.167183
$$323$$ 0 0
$$324$$ 1.00000 0.0555556
$$325$$ −12.5000 21.6506i −0.693375 1.20096i
$$326$$ −10.0000 17.3205i −0.553849 0.959294i
$$327$$ −5.50000 + 9.52628i −0.304151 + 0.526804i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 1.00000 0.0549650 0.0274825 0.999622i $$-0.491251\pi$$
0.0274825 + 0.999622i $$0.491251\pi$$
$$332$$ 3.00000 5.19615i 0.164646 0.285176i
$$333$$ −2.00000 + 3.46410i −0.109599 + 0.189832i
$$334$$ −12.0000 −0.656611
$$335$$ 0 0
$$336$$ −0.500000 + 0.866025i −0.0272772 + 0.0472456i
$$337$$ −2.00000 3.46410i −0.108947 0.188702i 0.806397 0.591375i $$-0.201415\pi$$
−0.915344 + 0.402673i $$0.868081\pi$$
$$338$$ −6.00000 + 10.3923i −0.326357 + 0.565267i
$$339$$ −3.00000 5.19615i −0.162938 0.282216i
$$340$$ 0 0
$$341$$ −24.0000 −1.29967
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ −4.00000 6.92820i −0.215666 0.373544i
$$345$$ 0 0
$$346$$ 3.00000 5.19615i 0.161281 0.279347i
$$347$$ −9.00000 15.5885i −0.483145 0.836832i 0.516667 0.856186i $$-0.327172\pi$$
−0.999813 + 0.0193540i $$0.993839\pi$$
$$348$$ −4.50000 + 7.79423i −0.241225 + 0.417815i
$$349$$ −10.0000 −0.535288 −0.267644 0.963518i $$-0.586245\pi$$
−0.267644 + 0.963518i $$0.586245\pi$$
$$350$$ 5.00000 0.267261
$$351$$ 12.5000 21.6506i 0.667201 1.15563i
$$352$$ 3.00000 5.19615i 0.159901 0.276956i
$$353$$ −15.0000 −0.798369 −0.399185 0.916871i $$-0.630707\pi$$
−0.399185 + 0.916871i $$0.630707\pi$$
$$354$$ 9.00000 0.478345
$$355$$ 0 0
$$356$$ −6.00000 10.3923i −0.317999 0.550791i
$$357$$ −1.50000 + 2.59808i −0.0793884 + 0.137505i
$$358$$ 0 0
$$359$$ −10.5000 18.1865i −0.554169 0.959849i −0.997968 0.0637221i $$-0.979703\pi$$
0.443799 0.896126i $$-0.353630\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ −2.00000 −0.105118
$$363$$ 12.5000 + 21.6506i 0.656080 + 1.13636i
$$364$$ −2.50000 4.33013i −0.131036 0.226960i
$$365$$ 0 0
$$366$$ −5.00000 8.66025i −0.261354 0.452679i
$$367$$ 14.0000 24.2487i 0.730794 1.26577i −0.225750 0.974185i $$-0.572483\pi$$
0.956544 0.291587i $$-0.0941834\pi$$
$$368$$ 3.00000 0.156386
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 1.50000 2.59808i 0.0778761 0.134885i
$$372$$ −4.00000 −0.207390
$$373$$ −23.0000 −1.19089 −0.595447 0.803394i $$-0.703025\pi$$
−0.595447 + 0.803394i $$0.703025\pi$$
$$374$$ 9.00000 15.5885i 0.465379 0.806060i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −22.5000 38.9711i −1.15881 2.00712i
$$378$$ 2.50000 + 4.33013i 0.128586 + 0.222718i
$$379$$ 7.00000 0.359566 0.179783 0.983706i $$-0.442460\pi$$
0.179783 + 0.983706i $$0.442460\pi$$
$$380$$ 0 0
$$381$$ 2.00000 0.102463
$$382$$ −1.50000 2.59808i −0.0767467 0.132929i
$$383$$ 9.00000 + 15.5885i 0.459879 + 0.796533i 0.998954 0.0457244i $$-0.0145596\pi$$
−0.539076 + 0.842257i $$0.681226\pi$$
$$384$$ 0.500000 0.866025i 0.0255155 0.0441942i
$$385$$ 0 0
$$386$$ 7.00000 12.1244i 0.356291 0.617113i
$$387$$ −16.0000 −0.813326
$$388$$ 10.0000 0.507673
$$389$$ −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i $$-0.984165\pi$$
0.542445 + 0.840091i $$0.317499\pi$$
$$390$$ 0 0
$$391$$ 9.00000 0.455150
$$392$$ −6.00000 −0.303046
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −6.00000 10.3923i −0.301511 0.522233i
$$397$$ −10.0000 17.3205i −0.501886 0.869291i −0.999998 0.00217869i $$-0.999307\pi$$
0.498112 0.867113i $$-0.334027\pi$$
$$398$$ 11.0000 0.551380
$$399$$ 0 0
$$400$$ −5.00000 −0.250000
$$401$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$402$$ −2.50000 4.33013i −0.124689 0.215967i
$$403$$ 10.0000 17.3205i 0.498135 0.862796i
$$404$$ −9.00000 15.5885i −0.447767 0.775555i
$$405$$ 0 0
$$406$$ 9.00000 0.446663
$$407$$ 12.0000 0.594818
$$408$$ 1.50000 2.59808i 0.0742611 0.128624i
$$409$$ 16.0000 27.7128i 0.791149 1.37031i −0.134107 0.990967i $$-0.542817\pi$$
0.925256 0.379344i $$-0.123850\pi$$
$$410$$ 0 0
$$411$$ 9.00000 0.443937
$$412$$ 7.00000 12.1244i 0.344865 0.597324i
$$413$$ −4.50000 7.79423i −0.221431 0.383529i
$$414$$ 3.00000 5.19615i 0.147442 0.255377i
$$415$$ 0 0
$$416$$ 2.50000 + 4.33013i 0.122573 + 0.212302i
$$417$$ 4.00000 0.195881
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ 8.50000 + 14.7224i 0.414265 + 0.717527i 0.995351 0.0963145i $$-0.0307055\pi$$
−0.581086 + 0.813842i $$0.697372\pi$$
$$422$$ 2.50000 4.33013i 0.121698 0.210787i
$$423$$ 0 0
$$424$$ −1.50000 + 2.59808i −0.0728464 + 0.126174i
$$425$$ −15.0000 −0.727607
$$426$$ −6.00000 −0.290701
$$427$$ −5.00000 + 8.66025i −0.241967 + 0.419099i
$$428$$ −4.50000 + 7.79423i −0.217516 + 0.376748i
$$429$$ −30.0000 −1.44841
$$430$$ 0 0
$$431$$ 3.00000 5.19615i 0.144505 0.250290i −0.784683 0.619897i $$-0.787174\pi$$
0.929188 + 0.369607i $$0.120508\pi$$
$$432$$ −2.50000 4.33013i −0.120281 0.208333i
$$433$$ 1.00000 1.73205i 0.0480569 0.0832370i −0.840996 0.541041i $$-0.818030\pi$$
0.889053 + 0.457804i $$0.151364\pi$$
$$434$$ 2.00000 + 3.46410i 0.0960031 + 0.166282i
$$435$$ 0 0
$$436$$ −11.0000 −0.526804
$$437$$ 0 0
$$438$$ 7.00000 0.334473
$$439$$ −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i $$-0.933739\pi$$
0.310228 0.950662i $$-0.399595\pi$$
$$440$$ 0 0
$$441$$ −6.00000 + 10.3923i −0.285714 + 0.494872i
$$442$$ 7.50000 + 12.9904i 0.356739 + 0.617889i
$$443$$ 9.00000 15.5885i 0.427603 0.740630i −0.569057 0.822298i $$-0.692691\pi$$
0.996660 + 0.0816684i $$0.0260248\pi$$
$$444$$ 2.00000 0.0949158
$$445$$ 0 0
$$446$$ 13.0000 22.5167i 0.615568 1.06619i
$$447$$ 0 0
$$448$$ −1.00000 −0.0472456
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ −5.00000 + 8.66025i −0.235702 + 0.408248i
$$451$$ 0 0
$$452$$ 3.00000 5.19615i 0.141108 0.244406i
$$453$$ 5.00000 + 8.66025i 0.234920 + 0.406894i
$$454$$ −7.50000 12.9904i −0.351992 0.609669i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 17.0000 0.795226 0.397613 0.917553i $$-0.369839\pi$$
0.397613 + 0.917553i $$0.369839\pi$$
$$458$$ 11.0000 + 19.0526i 0.513996 + 0.890268i
$$459$$ −7.50000 12.9904i −0.350070 0.606339i
$$460$$ 0 0
$$461$$ 6.00000 + 10.3923i 0.279448 + 0.484018i 0.971248 0.238071i $$-0.0765153\pi$$
−0.691800 + 0.722089i $$0.743182\pi$$
$$462$$ 3.00000 5.19615i 0.139573 0.241747i
$$463$$ −4.00000 −0.185896 −0.0929479 0.995671i $$-0.529629\pi$$
−0.0929479 + 0.995671i $$0.529629\pi$$
$$464$$ −9.00000 −0.417815
$$465$$ 0 0
$$466$$ 3.00000 5.19615i 0.138972 0.240707i
$$467$$ 18.0000 0.832941 0.416470 0.909149i $$-0.363267\pi$$
0.416470 + 0.909149i $$0.363267\pi$$
$$468$$ 10.0000 0.462250
$$469$$ −2.50000 + 4.33013i −0.115439 + 0.199947i
$$470$$ 0 0
$$471$$ −11.0000 + 19.0526i −0.506853 + 0.877896i
$$472$$ 4.50000 + 7.79423i 0.207129 + 0.358758i
$$473$$ 24.0000 + 41.5692i 1.10352 + 1.91135i
$$474$$ −10.0000 −0.459315
$$475$$ 0 0
$$476$$ −3.00000 −0.137505
$$477$$ 3.00000 + 5.19615i 0.137361 + 0.237915i
$$478$$ 10.5000 + 18.1865i 0.480259 + 0.831833i
$$479$$ −18.0000 + 31.1769i −0.822441 + 1.42451i 0.0814184 + 0.996680i $$0.474055\pi$$
−0.903859 + 0.427830i $$0.859278\pi$$
$$480$$ 0 0
$$481$$ −5.00000 + 8.66025i −0.227980 + 0.394874i
$$482$$ −8.00000 −0.364390
$$483$$ 3.00000 0.136505
$$484$$ −12.5000 + 21.6506i −0.568182 + 0.984120i
$$485$$ 0 0
$$486$$ −16.0000 −0.725775
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ 5.00000 8.66025i 0.226339 0.392031i
$$489$$ 10.0000 + 17.3205i 0.452216 + 0.783260i
$$490$$ 0 0
$$491$$ 18.0000 + 31.1769i 0.812329 + 1.40699i 0.911230 + 0.411897i $$0.135134\pi$$
−0.0989017 + 0.995097i $$0.531533\pi$$
$$492$$ 0 0
$$493$$ −27.0000 −1.21602
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −2.00000 3.46410i −0.0898027 0.155543i
$$497$$ 3.00000 + 5.19615i 0.134568 + 0.233079i
$$498$$ −3.00000 + 5.19615i −0.134433 + 0.232845i
$$499$$ 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i $$-0.138129\pi$$
−0.817781 + 0.575529i $$0.804796\pi$$
$$500$$ 0 0
$$501$$ 12.0000 0.536120
$$502$$ 6.00000 0.267793
$$503$$ 10.5000 18.1865i 0.468172 0.810897i −0.531167 0.847267i $$-0.678246\pi$$
0.999338 + 0.0363700i $$0.0115795\pi$$
$$504$$ −1.00000 + 1.73205i −0.0445435 + 0.0771517i
$$505$$ 0 0
$$506$$ −18.0000 −0.800198
$$507$$ 6.00000 10.3923i 0.266469 0.461538i
$$508$$ 1.00000 + 1.73205i 0.0443678 + 0.0768473i
$$509$$ 15.0000 25.9808i 0.664863 1.15158i −0.314459 0.949271i $$-0.601823\pi$$
0.979322 0.202306i $$-0.0648436\pi$$
$$510$$ 0 0
$$511$$ −3.50000 6.06218i −0.154831 0.268175i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −12.0000 −0.529297
$$515$$ 0 0
$$516$$ 4.00000 + 6.92820i 0.176090 + 0.304997i
$$517$$ 0 0
$$518$$ −1.00000 1.73205i −0.0439375 0.0761019i
$$519$$ −3.00000 + 5.19615i −0.131685 + 0.228086i
$$520$$ 0 0
$$521$$ 36.0000 1.57719 0.788594 0.614914i $$-0.210809\pi$$
0.788594 + 0.614914i $$0.210809\pi$$
$$522$$ −9.00000 + 15.5885i −0.393919 + 0.682288i
$$523$$ 5.50000 9.52628i 0.240498 0.416555i −0.720358 0.693602i $$-0.756023\pi$$
0.960856 + 0.277047i $$0.0893559\pi$$
$$524$$ 0 0
$$525$$ −5.00000 −0.218218
$$526$$ −12.0000 + 20.7846i −0.523225 + 0.906252i
$$527$$ −6.00000 10.3923i −0.261364 0.452696i
$$528$$ −3.00000 + 5.19615i −0.130558 + 0.226134i
$$529$$ 7.00000 + 12.1244i 0.304348 + 0.527146i
$$530$$ 0 0
$$531$$ 18.0000 0.781133
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 6.00000 + 10.3923i 0.259645 + 0.449719i
$$535$$ 0 0
$$536$$ 2.50000 4.33013i 0.107984 0.187033i
$$537$$ 0 0
$$538$$ −3.00000 + 5.19615i −0.129339 + 0.224022i
$$539$$ 36.0000 1.55063
$$540$$ 0 0
$$541$$ −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i $$-0.847023\pi$$
0.843728 + 0.536771i $$0.180356\pi$$
$$542$$ −5.50000 + 9.52628i −0.236245 + 0.409189i
$$543$$ 2.00000 0.0858282
$$544$$ 3.00000 0.128624
$$545$$ 0 0
$$546$$ 2.50000 + 4.33013i 0.106990 + 0.185312i
$$547$$ 22.0000 38.1051i 0.940652 1.62926i 0.176421 0.984315i $$-0.443548\pi$$
0.764231 0.644942i $$-0.223119\pi$$
$$548$$ 4.50000 + 7.79423i 0.192230 + 0.332953i
$$549$$ −10.0000 17.3205i −0.426790 0.739221i
$$550$$ 30.0000 1.27920
$$551$$ 0 0
$$552$$ −3.00000 −0.127688
$$553$$ 5.00000 + 8.66025i 0.212622 + 0.368271i
$$554$$ −4.00000 6.92820i −0.169944 0.294351i
$$555$$ 0 0
$$556$$ 2.00000 + 3.46410i 0.0848189 + 0.146911i
$$557$$ −12.0000 + 20.7846i −0.508456 + 0.880672i 0.491496 + 0.870880i $$0.336450\pi$$
−0.999952 + 0.00979220i $$0.996883\pi$$
$$558$$ −8.00000 −0.338667
$$559$$ −40.0000 −1.69182
$$560$$ 0 0
$$561$$ −9.00000 + 15.5885i −0.379980 + 0.658145i
$$562$$ 0 0
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 11.0000 19.0526i 0.462364 0.800839i
$$567$$ 0.500000 + 0.866025i 0.0209980 + 0.0363696i
$$568$$ −3.00000 5.19615i −0.125877 0.218026i
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ −15.0000 25.9808i −0.627182 1.08631i
$$573$$ 1.50000 + 2.59808i 0.0626634 + 0.108536i
$$574$$ 0 0
$$575$$ 7.50000 + 12.9904i 0.312772 + 0.541736i
$$576$$ 1.00000 1.73205i 0.0416667 0.0721688i
$$577$$ 11.0000 0.457936 0.228968 0.973434i $$-0.426465\pi$$
0.228968 + 0.973434i $$0.426465\pi$$
$$578$$ −8.00000 −0.332756
$$579$$ −7.00000 + 12.1244i −0.290910 + 0.503871i
$$580$$ 0 0
$$581$$ 6.00000 0.248922
$$582$$ −10.0000 −0.414513
$$583$$ 9.00000 15.5885i 0.372742 0.645608i
$$584$$ 3.50000 + 6.06218i 0.144831 + 0.250855i
$$585$$ 0 0
$$586$$ −10.5000 18.1865i −0.433751 0.751279i
$$587$$ 6.00000 + 10.3923i 0.247647 + 0.428936i 0.962872 0.269957i $$-0.0870095\pi$$
−0.715226 + 0.698893i $$0.753676\pi$$
$$588$$ 6.00000 0.247436
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 1.00000 + 1.73205i 0.0410997 + 0.0711868i
$$593$$ 15.0000 25.9808i 0.615976 1.06690i −0.374236 0.927333i $$-0.622095\pi$$
0.990212 0.139569i $$-0.0445716\pi$$
$$594$$ 15.0000 + 25.9808i 0.615457 + 1.06600i
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −11.0000 −0.450200
$$598$$ 7.50000 12.9904i 0.306698 0.531216i
$$599$$ −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i $$-0.996449\pi$$
0.509631 + 0.860393i $$0.329782\pi$$
$$600$$ 5.00000 0.204124
$$601$$ 28.0000 1.14214 0.571072 0.820900i $$-0.306528\pi$$
0.571072 + 0.820900i $$0.306528\pi$$
$$602$$ 4.00000 6.92820i 0.163028 0.282372i
$$603$$ −5.00000 8.66025i −0.203616 0.352673i
$$604$$ −5.00000 + 8.66025i −0.203447 + 0.352381i
$$605$$ 0 0
$$606$$ 9.00000 + 15.5885i 0.365600 + 0.633238i
$$607$$ 22.0000 0.892952 0.446476 0.894795i $$-0.352679\pi$$
0.446476 + 0.894795i $$0.352679\pi$$
$$608$$ 0 0
$$609$$ −9.00000 −0.364698
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 3.00000 5.19615i 0.121268 0.210042i
$$613$$ −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i $$-0.179527\pi$$
−0.885514 + 0.464614i $$0.846193\pi$$
$$614$$ 10.0000 17.3205i 0.403567 0.698999i
$$615$$ 0 0
$$616$$ 6.00000 0.241747
$$617$$ 3.00000 5.19615i 0.120775 0.209189i −0.799298 0.600935i $$-0.794795\pi$$
0.920074 + 0.391745i $$0.128129\pi$$
$$618$$ −7.00000 + 12.1244i −0.281581 + 0.487713i
$$619$$ −10.0000 −0.401934 −0.200967 0.979598i $$-0.564408\pi$$
−0.200967 + 0.979598i $$0.564408\pi$$
$$620$$ 0 0
$$621$$ −7.50000 + 12.9904i −0.300965 + 0.521286i
$$622$$ 10.5000 + 18.1865i 0.421012 + 0.729214i
$$623$$ 6.00000 10.3923i 0.240385 0.416359i
$$624$$ −2.50000 4.33013i −0.100080 0.173344i
$$625$$ −12.5000 21.6506i −0.500000 0.866025i
$$626$$ −19.0000 −0.759393
$$627$$ 0 0
$$628$$ −22.0000 −0.877896
$$629$$ 3.00000 + 5.19615i 0.119618 + 0.207184i
$$630$$ 0 0
$$631$$ 8.00000 13.8564i 0.318475 0.551615i −0.661695 0.749773i $$-0.730163\pi$$
0.980170 + 0.198158i $$0.0634960\pi$$
$$632$$ −5.00000 8.66025i −0.198889 0.344486i
$$633$$ −2.50000 + 4.33013i −0.0993661 + 0.172107i
$$634$$ 9.00000 0.357436
$$635$$ 0 0
$$636$$ 1.50000 2.59808i 0.0594789 0.103020i
$$637$$ −15.0000 + 25.9808i −0.594322 + 1.02940i
$$638$$ 54.0000 2.13788
$$639$$ −12.0000 −0.474713
$$640$$ 0 0
$$641$$ 3.00000 + 5.19615i 0.118493 + 0.205236i 0.919171 0.393860i $$-0.128860\pi$$
−0.800678 + 0.599095i $$0.795527\pi$$
$$642$$ 4.50000 7.79423i 0.177601 0.307614i
$$643$$ 11.0000 + 19.0526i 0.433798 + 0.751360i 0.997197 0.0748254i $$-0.0238399\pi$$
−0.563399 + 0.826185i $$0.690507\pi$$
$$644$$ 1.50000 + 2.59808i 0.0591083 + 0.102379i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 27.0000 1.06148 0.530740 0.847535i $$-0.321914\pi$$
0.530740 + 0.847535i $$0.321914\pi$$
$$648$$ −0.500000 0.866025i −0.0196419 0.0340207i
$$649$$ −27.0000 46.7654i −1.05984 1.83570i
$$650$$ −12.5000 + 21.6506i −0.490290 + 0.849208i
$$651$$ −2.00000 3.46410i −0.0783862 0.135769i
$$652$$ −10.0000 + 17.3205i −0.391630 + 0.678323i
$$653$$ 24.0000 0.939193 0.469596 0.882881i $$-0.344399\pi$$
0.469596 + 0.882881i $$0.344399\pi$$
$$654$$ 11.0000 0.430134
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 14.0000 0.546192
$$658$$ 0 0
$$659$$ −22.5000 + 38.9711i −0.876476 + 1.51810i −0.0212930 + 0.999773i $$0.506778\pi$$
−0.855183 + 0.518327i $$0.826555\pi$$
$$660$$ 0 0
$$661$$ −6.50000 + 11.2583i −0.252821 + 0.437898i −0.964301 0.264807i $$-0.914692\pi$$
0.711481 + 0.702706i $$0.248025\pi$$
$$662$$ −0.500000 0.866025i −0.0194331 0.0336590i
$$663$$ −7.50000 12.9904i −0.291276 0.504505i
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ 4.00000 0.154997
$$667$$ 13.5000 + 23.3827i 0.522722 + 0.905381i
$$668$$ 6.00000 + 10.3923i 0.232147 + 0.402090i
$$669$$ −13.0000 + 22.5167i −0.502609 + 0.870544i
$$670$$ 0 0
$$671$$ −30.0000 + 51.9615i −1.15814 + 2.00595i
$$672$$ 1.00000 0.0385758
$$673$$ −44.0000 −1.69608 −0.848038 0.529936i $$-0.822216\pi$$
−0.848038 + 0.529936i $$0.822216\pi$$
$$674$$ −2.00000 + 3.46410i −0.0770371 + 0.133432i
$$675$$ 12.5000 21.6506i 0.481125 0.833333i
$$676$$ 12.0000 0.461538
$$677$$ 33.0000 1.26829 0.634147 0.773213i $$-0.281352\pi$$
0.634147 + 0.773213i $$0.281352\pi$$
$$678$$ −3.00000 + 5.19615i −0.115214 + 0.199557i
$$679$$ 5.00000 + 8.66025i 0.191882 + 0.332350i
$$680$$ 0 0
$$681$$ 7.50000 + 12.9904i 0.287401 + 0.497792i
$$682$$ 12.0000 + 20.7846i 0.459504 + 0.795884i
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −6.50000 11.2583i −0.248171 0.429845i
$$687$$ −11.0000 19.0526i −0.419676 0.726900i
$$688$$ −4.00000 + 6.92820i −0.152499 + 0.264135i
$$689$$ 7.50000 + 12.9904i 0.285727 + 0.494894i
$$690$$ 0 0
$$691$$ −10.0000 −0.380418 −0.190209 0.981744i $$-0.560917\pi$$
−0.190209 + 0.981744i $$0.560917\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 6.00000 10.3923i 0.227921 0.394771i
$$694$$ −9.00000 + 15.5885i −0.341635 + 0.591730i
$$695$$ 0 0
$$696$$ 9.00000 0.341144
$$697$$ 0 0
$$698$$ 5.00000 + 8.66025i 0.189253 + 0.327795i
$$699$$ −3.00000 + 5.19615i −0.113470 + 0.196537i
$$700$$ −2.50000 4.33013i −0.0944911 0.163663i
$$701$$ −6.00000 10.3923i −0.226617 0.392512i 0.730186 0.683248i $$-0.239433\pi$$
−0.956803 + 0.290736i $$0.906100\pi$$
$$702$$ −25.0000 −0.943564
$$703$$ 0 0
$$704$$ −6.00000 −0.226134
$$705$$ 0 0
$$706$$ 7.50000 + 12.9904i 0.282266 + 0.488899i
$$707$$ 9.00000 15.5885i 0.338480 0.586264i
$$708$$ −4.50000 7.79423i −0.169120 0.292925i
$$709$$ 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i $$-0.773204\pi$$
0.944509 + 0.328484i $$0.106538\pi$$
$$710$$ 0 0
$$711$$ −20.0000 −0.750059
$$712$$ −6.00000 + 10.3923i −0.224860 + 0.389468i
$$713$$ −6.00000 + 10.3923i −0.224702 + 0.389195i
$$714$$ 3.00000 0.112272
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −10.5000 18.1865i −0.392130 0.679189i
$$718$$ −10.5000 + 18.1865i −0.391857 + 0.678715i
$$719$$ −19.5000 33.7750i −0.727227 1.25959i −0.958051 0.286599i $$-0.907475\pi$$
0.230823 0.972996i $$-0.425858\pi$$
$$720$$ 0 0
$$721$$ 14.0000 0.521387
$$722$$ 0 0
$$723$$ 8.00000 0.297523
$$724$$ 1.00000 + 1.73205i 0.0371647 + 0.0643712i
$$725$$ −22.5000 38.9711i −0.835629 1.44735i
$$726$$ 12.5000 21.6506i 0.463919 0.803530i
$$727$$ 18.5000 + 32.0429i 0.686127 + 1.18841i 0.973081 + 0.230463i $$0.0740239\pi$$
−0.286954 + 0.957944i $$0.592643\pi$$
$$728$$ −2.50000 + 4.33013i −0.0926562 + 0.160485i
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −12.0000 + 20.7846i −0.443836 + 0.768747i
$$732$$ −5.00000 + 8.66025i −0.184805 + 0.320092i
$$733$$ 32.0000 1.18195 0.590973 0.806691i $$-0.298744\pi$$
0.590973 + 0.806691i $$0.298744\pi$$
$$734$$ −28.0000 −1.03350
$$735$$ 0 0
$$736$$ −1.50000 2.59808i −0.0552907 0.0957664i
$$737$$ −15.0000 + 25.9808i −0.552532 + 0.957014i
$$738$$ 0 0
$$739$$ 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i $$-0.0715853\pi$$
−0.680534 + 0.732717i $$0.738252\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −3.00000 −0.110133
$$743$$ −18.0000 31.1769i −0.660356 1.14377i −0.980522 0.196409i $$-0.937072\pi$$
0.320166 0.947361i $$-0.396261\pi$$
$$744$$ 2.00000 + 3.46410i 0.0733236 + 0.127000i
$$745$$ 0 0
$$746$$ 11.5000 + 19.9186i 0.421045 + 0.729271i
$$747$$ −6.00000 + 10.3923i −0.219529 + 0.380235i
$$748$$ −18.0000 −0.658145
$$749$$ −9.00000 −0.328853
$$750$$ 0 0
$$751$$ −20.0000 + 34.6410i −0.729810 + 1.26407i 0.227153 + 0.973859i $$0.427058\pi$$
−0.956963 + 0.290209i $$0.906275\pi$$
$$752$$ 0 0
$$753$$ −6.00000 −0.218652
$$754$$ −22.5000 + 38.9711i −0.819402 + 1.41925i
$$755$$ 0 0
$$756$$ 2.50000 4.33013i 0.0909241 0.157485i
$$757$$ −1.00000 1.73205i −0.0363456 0.0629525i 0.847280 0.531146i $$-0.178238\pi$$
−0.883626 + 0.468193i $$0.844905\pi$$
$$758$$ −3.50000 6.06218i −0.127126 0.220188i
$$759$$ 18.0000 0.653359
$$760$$ 0 0
$$761$$ −21.0000 −0.761249 −0.380625 0.924730i $$-0.624291\pi$$
−0.380625 + 0.924730i $$0.624291\pi$$
$$762$$ −1.00000 1.73205i −0.0362262 0.0627456i
$$763$$ −5.50000 9.52628i −0.199113 0.344874i
$$764$$ −1.50000 + 2.59808i −0.0542681 + 0.0939951i
$$765$$ 0 0
$$766$$ 9.00000 15.5885i 0.325183 0.563234i
$$767$$ 45.0000 1.62486
$$768$$ −1.00000 −0.0360844
$$769$$ −2.50000 + 4.33013i −0.0901523 + 0.156148i −0.907575 0.419890i $$-0.862069\pi$$
0.817423 + 0.576038i $$0.195402\pi$$
$$770$$ 0 0
$$771$$ 12.0000 0.432169
$$772$$ −14.0000 −0.503871
$$773$$ 25.5000 44.1673i 0.917171 1.58859i 0.113480 0.993540i $$-0.463800\pi$$
0.803691 0.595047i $$-0.202867\pi$$
$$774$$ 8.00000 + 13.8564i 0.287554 + 0.498058i
$$775$$ 10.0000 17.3205i 0.359211 0.622171i
$$776$$ −5.00000 8.66025i −0.179490 0.310885i
$$777$$ 1.00000 + 1.73205i 0.0358748 + 0.0621370i
$$778$$ 18.0000 0.645331
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 18.0000 + 31.1769i